Inspired by our definition of boolean values, propose a data structure
capable of representing one of the two values `black` or `white`.
If we have
one of those values, call it a "black-or-white value", we should be able to
write:
the-value if-black if-white
(where `if-black` and `if-white` are anything), and get back one of `if-black` or
`if-white`, depending on which of the black-or-white values we started with. Give
a definition for each of `black` and `white`. (Do it in both lambda calculus
and also in Racket.)

Now propose a data structure capable of representing one of the three values
`red` `green` or `blue`, based on the same model. (Do it in both lambda
calculus and also in Racket.)

Pairs
-----
Recall our definitions of ordered pairs.
> the pair **(**x**,**y**)** is defined to be `\f. f x y`
To extract the first element of a pair p, you write:
p (\fst \snd. fst)
Here are some definitions in Racket:
(define make-pair (lambda (fst) (lambda (snd) (lambda (f) ((f fst) snd)))))
(define get-first (lambda (fst) (lambda (snd) fst)))
(define get-second (lambda (fst) (lambda (snd) snd)))
Now we can write:
(define p ((make-pair 10) 20))
(p get-first) ; will evaluate to 10
(p get-second) ; will evaluate to 20
If you're puzzled by having the pair to the left and the function that
operates on it come second, think about why it's being done this way: the pair
is a package that takes a function for operating on its elements *as an
argument*, and returns *the result of* operating on its elements with that
function. In other words, the pair is a higher-order function. (Consider the similarities between this definition of a pair and a generalized quantifier.)
If you like, you can disguise what's going on like this:
(define lifted-get-first (lambda (p) (p get-first)))
(define lifted-get-second (lambda (p) (p get-second)))
Now you can write:
(lifted-get-first p)
instead of:
(p get-first)
However, the latter is still what's going on under the hood. (Remark: `(lifted-f ((make-pair 10) 20))` stands to `(((make-pair 10) 20) f)` as `(((make-pair 10) 20) f)` stands to `((f 10) 20)`.)

Define a `dup` function that duplicates its argument to form a pair
whose elements are the same.
Expected behavior:
((dup 10) get-first) ; evaluates to 10
((dup 10) get-second) ; evaluates to 10

Define a `sixteen` function that makes
sixteen copies of its argument (and stores them in a data structure of
your choice).

Inspired by our definition of ordered pairs, propose a data structure capable of representing ordered triples. That is,
(((make-triple M) N) P)
should return an object that behaves in a reasonable way to serve as a triple. In addition to defining the `make-triple` function, you have to show how to extract elements of your triple. Write a `get-first-of-triple` function, that does for triples what `get-first` does for pairs. Also write `get-second-of-triple` and `get-third-of-triple` functions.

Write a function `second-plus-third` that when given to your triple, returns the result of adding the second and third members of the triple.
You can help yourself to the following definition:
(define add (lambda (x) (lambda (y) (+ x y))))